The most common operational definitions of FGs are based on the magnitude gap between the brightest member galaxy of the group/cluster and other galaxy sorted by their magnitude (\(\Delta m_{1,j}\) , where \(j\)  represent the j\(-th\)  ranked galaxy). In particular, [1]} suggested that a group or a cluster of galaxies should be classified as fossil if the magnitude gap between its two brightest members (\(\Delta m_{12}\) ) is larger than 2 magnitudes in the \(r-\) band. In addition, they also imposed that the two brightest galaxies should be located within half the (projected) virial radius (defined as \(r_{200}\) , the radius of a sphere which mean density is 200 times the critical density of the Universe). Another common definition is the one presented in [2]}: a group/cluster of galaxies is classified as fossil if the magnitude gap between its first and fourth brightest member galaxies (\(\Delta m_{14}\) ) is larger than 2.5 magnitudes in the \(r-\) band and within half the (projected) virial radius. Both definitions also require the presence of a diffuse X-ray halo, with \(L_X \ge 10^{42} \,h_{50}^{-2}\)  erg s\(^{-1}\) . This last criterium ensures that the system is located in a potential well similar in mass to groups or clusters of galaxies. An example of a typical FG and the color-magnitude diagram of its galaxy population is shown in Fig. REF .
